Story highlights

Privately, the campaign is in serious discussions about how to move forward.

There are two lines of thought within the campaign: getting out before Florida, and hanging in there

Alex Conant, Rubio's communications director, refuted CNN's reporting

Washington (CNN)A battle is being waged within Florida Sen. Marco Rubio's campaign about whether he should even remain in the Republican presidential race ahead of his home state primary on March 15, sources say.

Rubio himself is "bullish" on his odds of winning the critical primary, despite some advisers who are less hopeful and believe a loss there would damage him politically in both the short- and long-term.

Publicly, the campaign is maintaining they are still a contender in this race, touting a Sunday win in Puerto Rico's primary that delivered Rubio 23 delegates. But privately, the campaign is having a debate about whether he should remain in the mix -- even for his home state of Florida's primary.

"He doesn't want to get killed in his home state," one source familiar with the discussions said, noting "a poor showing would be a risk and hurt his political future."

Alex Conant, Rubio's communication director, said the report of such an internal debate is "100% false."

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"That is fiction," he told CNN's Wolf Blitzer on "The Situation Room."

"I was sitting in a senior staff meeting planning out next week's schedule when I saw this report suddenly air and I came racing across town to correct it," he added.

Conant pointed to the fact that Rubio appears to be closing in on GOP front-runner Donald Trump's lead in Florida.

A Monmouth poll released Monday shows Rubio behind Trump, 38% to 30%. A Quinnipiac poll released two weeks ago put Rubio behind Trump by a wider margin: 44% to 28%.

Most of the senator's advisers agree he does not have a path to the nomination and some are advising him to get out ahead of the March 15 primary.

Sources within the campaign also say the pressure will only continue to mount following an expected disappointing showing Tuesday, when voters in Michigan, Mississippi, Hawaii and Idaho make their picks in the GOP primary.

"Not going to have a great day is an understatement," one campaign source said.

Weighing the costs

There are two lines of thought within the campaign: getting out before Florida, and hanging in there.

On the one hand, some advisers are warning that if Rubio does poorly in his home state, it could not only hurt his presidential campaign but also his future politically, including a potential gubernatorial run in 2018 or chance to be on the ticket as a vice presidential candidate.

"Cruz won his home state. If Rubio can't win his, that's a problem," one prominent supporter said.

But others within the campaign are urging Rubio to stay in the race, predicting a better-than-expected finish in Florida.

Rubio's victory for his Senate seat against the governor makes him optimistic he can come from behind, said one source close to the campaign. The senator also believes his experience in the state translates to a superior ground game and infrastructure than that of his competitors.

The latter line of thinking seems to be winning, for the moment. But a particularly awful Tuesday could change the rationale, a source warned.

The endorsement game

One potential x-factor in the Florida contest is the looming possibility of an endorsement from once-rival Jeb Bush. But Rubio and Bush, the former Florida governor, have spoken three times since Bush dropped out of the 2016 last month and the Rubio campaign is not expecting an endorsement.

Rubio raised the possibility in the latter two conversations, sources said, but felt Bush was "vague about his interest" and Rubio came away under the impression that Bush would not endorse.

The fellow Floridian is a long-time friend and mentor of Rubio's, but they clashed as opponents during the GOP primary. Many of Bush's backers endorsed Rubio after the former governor departed the race, and others who had stayed out of it put their support behind Rubio.

But not all of Bush's supporters moved over, and some talk of bad blood has hung over the relationship between the two campaigns.

Romney role

Other political insiders are closely watching to see what former Massachusetts Gov. Mitt Romney decides to do. The 2012 GOP nominee delivered a speech last week excoriating Trump -- but he did not endorse any of the remaining Trump rivals.

Romney is going to continue with that anti-Trump campaign, a source close to the former governor said, adding that while he is not running, he is open to the possibility -- however remote -- of stepping into a brokered convention as a consensus pick.

Sources familiar say that Romney isn't working with any of the non-Trump campaigns, but part of his resistance to throwing his support behind one is to leave his own options open.